This dissertation examines the Appeals Process in the Brazilian deposit and its Application in Civil Procedure. Therefore, the research supports the appeal bond in the Brazilian Civil Procedure and microsystem of special civil courts, under the name of "civil appeal bond", as another procedural mechanism due to the slow processing of lawsuits in Brazil and future warranty implementing the actions of a pecuniary nature, bringing safety and speedy, fair and effective judicial protection and suggests a change in legislation, taking as an example the appeal bond of the Labour Process. At first, we analyze the main discussions around the appeal bond, namely: the general part, the various aspects of the slowness of justice, then the appeal bond in administrative processes, labor and civil, as to its concept, historicity, legality, historical evolution, its purpose, legal, and other aspects. Finally, weave themselves considerations about the appeal bond in the Brazilian civil procedure, with the study and the reasons for its applicability in civil procedural law and special civil courts, showing the need for legislative amendment to insert the institute studied the Brazilian civil procedure.